I would have been confused myself.
Did you say that she said that you needed a bra so that you wouldn't be able to tell that you were braless?
Why wear a bra if you are going to be braless? I don't get that.
yes, I think that you missed a good chance to have a conversation about bralessness. You could have told her that you wanted to be braless and maybe she would have continued the discussion further.
Try not to avoid chances to have friendly conversations about being brafree with your lady friends and see what they have to say.